For filling: Position rack in center of oven and preheat to 300° F. Line bottom of 9-inch diameter springform pan with 2 ¾-inch high sides with waxed paper. Spray paper with nonstick vegetable spray. Using electric mixer, beat cream cheese and sugar in large bowl on low speed until smooth. Gradually mix in cocoa. Beat in eggs, 1 at a time. Gradually add cream, coffee liqueur, Frangelico and vanilla and beat until mixture is smooth.

Transfer filling to prepared pan. Bake until outer 3 inches of cake puff and center is gently set but moist looking, about 1 hour 30 minutes. Cool on rack. Cover and refrigerate until cake is well chilled, at least 6 hours. (can be prepared 1 day ahead)

For Glaze: Boil coffee liqueur, Frangelico and rum in heavy medium saucepan until reduced to ¼ cup, about 3 minutes. Reduce heat to low and add chocolate, cream, and butter. Stir until mixture is smooth. Cool until mixture is thick but still pourable, stirring occasionally, about 45 minutes. Using small sharp knife, cut around pan sides to loosen cake. Release and remove pan sides. Pour chocolate glaze over cake. Spread smoothly over top and sides covering completely. Chill until chocolate is firm, at least 2 hours.